Do adults in Japan watch anime?

Is anime just a kid thing, or are there adults in Japan that watch anime too? I heard it's looked down upon if you're over the age of 18 and you still watch anime. I think that some of the more provocative anime like Elfen Lied would be more geared towards adults.

Anime is not a kid thing. It's an otaku (geek) thing. They show a lot of them after midnight for those who'd rather watch anime than get some beauty sleep for tomorrow's work. So it's looked down upon if you're over the age of 18 and you still watch anime.

I guess it depends on the anime and on how frequently you watch.

Ghibli films for example are very popular even among adults. At least when I went to see Ghibli films in the cinema the audience was always very mixed.

If you don't watch anime excessively or talk about it all the time you won't be considered an otaku.

I think that some of the more provocative anime like Elfen Lied would be more geared towards adults.

Yes, but it does not mean many Japanese adults watch such anime titles.
They are geard only towards anime-addicted adults.
Many Japanese adults even don't know existence of such anime.

It depends just on the person.
There excist several adults in Japan who watch anime and several who don't watch.